scholarly journals Analysis of the long-time asymptotic behaviour of the solution of a two-dimensional reaction-diffusion equation

2015 ◽  
Vol 4 (2) ◽  
pp. 332
Author(s):  
Joel Ndam
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Asymptotic Behaviour ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Variable Diffusion Coefficient ◽  
Long Time ◽  
Variable Diffusion

<p>A reaction-diffusion equation in two dimensions is considered. The long-time asymptotic behaviour of the solution of this equation is examined in terms of uniform diffusion as well as density-dependent diffusion. The results show that in both cases, the solution attains a steady state, but does so more slowly with the variable diffusion coefficient when its magnitude d&lt;1.</p>

Description of segregation in a horizontal drum mixer by use of the diffusion equation

1988 ◽  
Vol 53 (4) ◽  
pp. 771-787 ◽  
Author(s):  
Vladimír Kudrna ◽  
Andrzej Rochowiecki
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Two Dimensions ◽  
Solid Particles ◽  
Axial Segregation ◽  
Variable Diffusion Coefficient ◽  
Drum Mixer ◽  
Forward Diffusion ◽  
Variable Diffusion ◽  
Horizontal Drum

An attempt has been made to describe the axial segregation of solid particles of two dimensions in a horizontal drum mixer. For this purpose the Kolmogorov's forward diffusion equation with variable diffusion coefficient and zero drift velocity was used. For the case of "pure" segregation this approach has given good results.

scholarly journals Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Ramezani
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
B Spline ◽  
Computational Work ◽  
Distributed Order ◽  
Fractional Reaction

AbstractThe main propose of this paper is presenting an efficient numerical scheme to solve WSGD scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation. The proposed method is based on fractional B-spline basics in collocation method which involve Caputo-type fractional derivatives for $$0 < \alpha < 1$$ 0 < α < 1 . The most significant privilege of proposed method is efficient and quite accurate and it requires relatively less computational work. The solution of consideration problem is transmute to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. The finally, several numerical WSGD Scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation.

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